Demian Bichir, the Mexican film star, stood in my kitchen at lunchtime testing the pile of avocados on the counter. He wanted to make guacamole the way he used to as a busboy at Rosa Mexicano in the 1980s, during his first sustained lap as an actor in the United States. Instead of a contrived lunch date at a restaurant, digital recorders whirring, he decided to come over to my apartment with a bottle of Patrón tequila and his hands ready for cooking.

I had prepared the molcajete, the traditional Mexican version of a mortar and pestle, and gathered the onions, cilantro, tomatoes, jalapeños, avocados and habaneros. (“Habaneros?” he said. “If you want to kill somebody.”) I stashed the tequila in the freezer.

“This one doesn’t feel right,” he said, touching an avocado’s papery skin. “But this guy, and this guy” — he reached for another and, squinting, palmed the fruit as gently as if it were a bird’s egg ready to hatch — “and this guy are perfect.” Within a second, a six-inch Wüsthof cook’s knife had sliced the avocado in half and Bichir, looking into my eyes, brought down the knife into the palm of his hand with a thwap.

Oh, God. Do we call an ambulance?

No. Locking the pit onto the blade of the knife, he worked it free in a deft corkscrew motion, accompanying his Kabuki with sound effects. “Poom, poom, poom. Whish.” He cross-hatched each side — “pap, pap, pap” — and spooned out the perfect square chunks into the molcajete.

Delicacy, precision, startling force: these are qualities that defined Bichir’s performance in “A Better Life,” a remarkable film that has cemented his reputation as a formidable talent in Hollywood. A household name in Mexico for two decades, he has become familiar to American audiences in recent years as Fidel Castro in Steven Soderbergh’s “Che” and as the brutally handsome, morally Manichean mayor of Tijuana and husband to Mary-Louise Parker in Showtime’s totally twisted, insanely entertaining Emmy-winning series “Weeds.”

The son of a Mexican theater director and an actress, Bichir is one of three acting brothers — Odiseo, Demian and Bruno— so famous for their prolific output that in 2003 the Mexican MTV Movie Awards created the category “Best Bichir in a Movie.” (Demian won.) He grew up in the barrios of Mexico City, poor but surrounded by books. “My parents met in the theater, and they grew up loving theater, and when my brothers and I decided to become actors, we had all we needed in our library at home,” he said.

In “A Better Life,” Bichir is Carlos Galindo, an illegal immigrant from Mexico who scrapes out an existence as a gardener, peering in at an American dream of swimming pools, housekeepers and big cars in the Hollywood Hills. When Carlos’s sister lends him enough money to buy a truck, which would catapult him from day laborer to gardening boss, he hesitates: she hasn’t told her husband she has taken the money out of their savings account. And there is so much more at stake. Carlos has no driver’s license, so being pulled over means instant arrest, deportation and separation from his son, whom he has raised as a single father.

He buys the truck; the next day, in an act of insidious betrayal, it is stolen. One of the tougher scenes to watch is one in which Carlos stands on a busy street, his work clothes briny with sweat, his eyes fruitlessly searching the traffic for his truck — the dream that will rescue him and his child from their gang-controlled East L.A. barrio, that will allow them to live in a house with more than one bed and one sofa. His eyes alight on a police officer, yet he can’t ask for help. In Bichir’s face, we see that Carlos knows his situation is utterly futile, and he and his child are vulnerable. The sense of despair and desperation is all-encompassing.

Bichir calls it one of the most important works of his career, “and for an actor,” he added, “the character of Carlos Galindo has the same dimension and depth as Lear or Hamlet — it’s that powerful.” When he first met with Chris Weitz — whose grandmother Lupita Tovar was perhaps Mexico’s most famous actress — the director told Bichir that he was not going to make an overtly political film, but that he would set out to present a simple, powerful story that happened to have as one of its themes the Mexican immigrant experience.

“I didn’t see any gimmicks, any Hollywood tricks,” Bichir said. “I need to be moved and for something to speak to me truthfully.”

While the movie is political, certainly, Weitz (director of “About a Boy,” “The Golden Compass” and “The Twilight Saga: New Moon”) chose to tell the story of Carlos Galindo as a piece of social realism, rather than as political propaganda. However, as Weitz told me, “the moment you train a camera on someone, especially a film camera, you say they are worthy of being paid attention to, and it elicits sympathy. In that regard, the film is political by default.” But he chose not to push that button too hard and risk “turning Carlos into a symbol rather than a closely observed character,” he said. In that sense, “A Better Life” is a story about the delicate relationship between a father and son, about loss of culture, about isolation, about the spiritual lives of two nations.

Bichir moved to New York when he was 22. “My mother said, ‘What? You can’t move there! They shoot people at 2 o’clock in the afternoon! Oh my God!’ ” He auditioned at Lee Strasberg and was told he was already an actor and he should save the $5,000 tuition. “And that’s when I stopped acting,” he said. “I wanted to give my actor a break. I wanted to live and to learn English. I wanted to be anything, a cabdriver, a busboy, anything to keep me away from acting for a while.”

Thus, his stretch as a busboy at Rosa Mexicano, where his job included making guacamole in front of each customer’s table. “I think I still hold the record for making 39 guacamoles in one lunch,” he said. Then on to Los Angeles, where he spent four years going on auditions and trying to land a role. “Nothing happened,” he said. “It was hard, really hard.” When he was offered a role in “Hasta Morir,” he took it, returning to Mexico, where he won an Ariel, the Mexican equivalent of an Oscar.

In Mexico, he worked all the time. “And then one day, I was about 41, and I pictured my life,” he said. “Soon, I would be living in a house with a big swimming pool, drinking a bloody mary and thinking, what if I had tried a little harder? Been a little more adventurous? Tried a little longer?” Divorced, with no attachments, he moved back to L.A. “Something had fundamentally changed in me, in my hard drive.”

While serving on the jury at the Ibiza Film Festival, he got a call at 5 in the morning from Steven Soderbergh, who asked him to play Castro in his biopic about Che Guevara. “And that was when it all began,” he said. “That was when everything changed.”

I first met Bichir before a screening of “A Better Life” in New York. Slender, animated, almost impish, his green eyes alight, he reminded me of a self-effacing Fred Astaire. “I’m writing a serious piece about you,” I said. “Because I’m — such—_ a serious actor?” Each word dropped with a beat of expert comic timing, as if to say: I. Am. Not. A. Serious. Actor. Lady. Get. A. Life.

As the film began, I couldn’t place the man I had just met on the screen. The wiry, bright-eyed comic in the lobby was replaced by a heavyset man whose face had been eaten away by weariness and fear, his eyes dull, the barest flicker of light left in them to suggest his soul was still alive way down inside.

Bichir is somewhat of a Method actor: he immersed himself in a life like Galindo’s by driving a gardener’s truck — which he bought off the street from some paisanos — wearing the same unwashed clothes for days, sleeping four hours a night. One of the film’s producers told me that two Mexicans spotted Bichir in L.A., in his gardener’s truck and shook their heads, saying, “Look, man! That’s Demian Bichir. He’s sure fallen on hard times.”

Yet he has such a light, comic gift, it was hard to watch him make guacamole and think that this was the same man who so brilliantly captured Castro’s threatening physicality, the curlicued accent, the voice veering from thunderous to almost ethereal, the powder-keg personality. Difficult to imagine this funny guy dancing salsa in my kitchen to Akwid’s “California” (a song from the soundtrack to “A Better Life”) as the gangster mayor who orders murders and makes a point to his pregnant girlfriend by basically raping her over his desk.

“It is extraordinary, Demian’s vitality in contrast to the performance he gives,” Weitz said. “All of the energy goes underground.” Benicio del Toro, who worked with Bichir on “Che,” describes him as one of the strongest actors he’s worked with. For the part of Castro, del Toro said, Soderbergh “needed someone who was strong but not someone who looked like he was acting strong. And that is kind of hard to find. Pacino can be strong without acting strong. Hoffman, too. Bichir has that quality, that gravitas.”

“We all have that capacity, to be two things,” Bichir said. “And after all I was named for both the devil and the angel. Demonio y angel. Dem-y-an.” (His parents took his name from the Herman Hesse novel “Demian: The Story of Emil Sinclair’s Youth.”)

Oliver Stone was drawn to the demonic side, and cast Bichir as a huckster in his next movie, “Savages,” based on a Don Winslow novel about pot growers and Mexican drug cartels. “He can play heavy,” Stone said, adding that “all he needs is one big role as a narcotraficante and if he hits that note just right he will have a worldwide reputation in a second.”

Everett CollectionBichir in his role as a drug dealer and mayor of Tijuana in “Weeds.”

Mary-Louise Parker, who played his lover and then wife on “Weeds,” also believes he plays good guys, like Carlos Galindo, with an almost sacred perfection. “I might use a word that sounds pretentious, but his performance was almost holy,” she said. “It was beyond being just about depth. He made the film into a Greek tragedy. And he is one of the few actors I know who could make that part humane.” And this from a woman who broke her toe during their first, unexpectedly vigorous love scene. “He is pretty delicious,” she added.

Bichir is dating but admits he is “really bad at long-term commitments.” He did become a father in May; the child is the product of a brief — “and beautiful, please, beautiful, beautiful” — romance in Spain last year. “I try to be as clear as I can be,” he said. “I don’t hide or play stupid games. I try to let everyone know that eventually I will probably be leaving.” In this case, a couple of months after his leave-taking, he got an e-mail informing him he would be a father. Bichir attended the baby’s birth, and she has his surname. “I decided to be there and not run away from the situation. I am her father, and I will love her forever,” he said.

At 48, Bichir feels as if he has experienced a kind of rebirth. “It is a before-and-after moment, for sure,” he said. After the meal and almost an entire bottle of tequila, we were looking out at the city. It was late afternoon. His roles as Castro, as Carlos Galindo and as Miguel Hidalgo in a Mexican production out this year about the country’s founder, are the work he is proudest of. “It would be sad,” he said, “if my best work had been 20 years ago and now I only had memories.”